CN108462191A - One kind being based on O3The low-frequency oscillation of electric power system discrimination method of KID algorithms - Google Patents
One kind being based on O3The low-frequency oscillation of electric power system discrimination method of KID algorithms Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The present invention relates to one kind being based on O3The low-frequency oscillation of electric power system discrimination method of KID algorithms.This method embedded observer in electric system stochastic model, utilize the Markov parameters and residual error of O3KID algorithms fundamental equation and Least Square Method observer, the identification of electric system stochastic system is converted to the identification problem of deterministic system, introduced observer is equivalent to Kalman filter.Hankel matrixes are constructed respectively using the output and residual error time series of observer, rectangular projection using deterministic system and singular value decomposition method, effective Identification of Power System reduced-order model, the accurate frequency, damping ratio and modal parameters information for extracting low-frequency oscillation dominant mode.The method of the present invention is suitable for the low-frequency oscillation of electric power system model analysis of WAMS synchronous measure environmental excitation signals and transient state ring down signals, and the emulation of 39 node systems of IEEE and the analysis of eastern United States power grid WAMS measured datas demonstrate the validity of this method.
Description
Technical field
The present invention relates to low-frequency oscillation analysis technical fields, especially a kind of to be based on O3The electric power of KID algorithms
Low frequency oscillations discrimination method.
Background technology
With the fast development of modern power systems, quick response excitation system extensive use, great Qu electricity in synchronous generator
Force system interconnects and grid-connected power generation system installed capacity proportion is constantly promoted, the power grid underdamping low-frequency oscillation thus caused
Problem is increasingly prominent, and the serious power transmission for restricting transmission line of electricity influences stable operation and the utility power quality control of electric system.
Currently, the extensive use of Wide Area Measurement System (wide areamonitoring system, WAMS), especially phasor measurement list
The continuous improvement of first (phasor measurement units, PMU) sample frequency and precision, for the low frequency measured based on data
Oscillation near real-time identification provides Informational support.
Mode point mainly is carried out to WAMS synchronous measure oscillation track signals based on the low-frequency oscillation identification that data measure
Analysis.The report speed of current main-stream PMU gathered datas is capable of the low-frequency oscillation dynamic of continuous record electricity system up to 100Hz
Process captures power grid environment pumping signal and transient state ring-down signals.Electric system is that a highly complex multi input is more
Output system, by the continuous pump of high independence multiple random signal, it tends to be difficult to accurate extraction system quasi-steady-state response, simultaneously
What the low-frequency oscillation trajectory signal of slow-decay also contributed to model determines rank, can not ensure the accuracy of modal identification.Kalman
Filtering method can effectively obtain the optimal State Estimation of linear stochaastic system, be suitable for engineer application.It is defeated using Kalman filtering
The normalization gone out, which newly ceases vector, has the characteristics that zero-mean white noise, by newly ceasing power spectral density statistical analysis, realizing electricity
The quick detection of Force system low-frequency oscillation modal damping Parameters variation, but essence is still a kind of nonparametric identification method.Karr
Graceful filtering and its extended method are extracted by establishing the transient state low-frequency oscillation response signal under linear filter Analyze noise environment
Leading Oscillatory mode shape parameter, it is still necessary to use accurate electric network model, the not applicable Low Frequency Oscillation Analysis measured based on data.It will
The OKID (observer/Kalmanfilteridentification, OKID) that observer is combined with characteristic value implementation method
Algorithm has become a kind of effective Identification of Linear Systems method, has successful application in input-output system identification.Needle
To electric system feature, the O that can further recognize only output system3KID algorithms are recognized for low-frequency oscillation of electric power system.
Invention content
The purpose of the present invention is to provide one kind being based on O3The low-frequency oscillation of electric power system discrimination method of KID algorithms, the party
Method embedded observer in electric system stochastic model, is effectively estimated observer Markov parameters and residual sequence, by power train
System stochastic system identification problem is converted to the identification problem of deterministic system, and introduced observer is equivalent to Kalman's filter
Wave device；Feature based on sciagraphy realizes the dominant mode parameter information of extraction low-frequency oscillation of electric power system.
To achieve the above object, the technical scheme is that：One kind being based on O3The low-frequency oscillation of electric power system of KID algorithms
Discrimination method, embedded observer, utilizes O in electric system stochastic model3KID algorithms fundamental equation and Least Square Method
The identification of electric system stochastic system is converted to the identification problem of deterministic system, institute by the Markov parameters and residual error of observer
The observer of introducing is equivalent to Kalman filter；It is described to utilize O3KID algorithms fundamental equation and Least Square Method observation
The Markov parameters of device and residual error the specific implementation process is as follows：
Step S1, the output observer model of following form is built：
Wherein,WithThe respectively state vector and output vector of observer, Μ are observer gain matrix；
Step S2, output estimation error vector is definedThe observer model of formula (1) can be rewritten as：
In formula
Step S3, by formula (2), recursion p-1 is walked forward, can be obtained：
Wherein：
O3KID algorithms use eigenvalue assignment method, by adjusting gain matrix K, by the pole of observer sytem matrix A
It is configured to z-plane origin, constitutes the progressive stable state observer of least beat；From Hamilton-Cayley theorems：Meeting p ＞
Under the conditions of ＞ n, haveTherefore formula (3) can be reduced to：
Step S4, substituting into formula (4) in formula (3) can obtain：
Y (k)=Φ v (k)+ε (k) (5)
Φ is that observer Markov joins sequence in formula, i.e. discrete unit impulse response samples；Formula (5) characterizes linear system
The autoregression relationship between output can be measured, for k=p, p+1 ..., l-1
Y=Φ V+E
In formula：
Y=[y (p) y (p+1) ... y (l-1)]
V=[v (p) v (p+1) ... v (l-1)]
E=[ε (p) ε (p+1) ... ε (l-1)]
Formula Y=Φ V+E are the fundamental equations of O3KID algorithms, and wherein Y and V are made of scalable system output, and E is
Output error matrix；
Step S5, the least squares estimator of observer Markov parametersIt is represented by：
Wherein, symbolThe generalized inverse of representing matrix, the error matrix estimator of outputIt can be written as：
Observer Markov parametersIt is uniquely determined by scalable system output time series, output errorBeing also can
Estimation, thus convert the identification of electric system stochastic system to deterministic system identification problem.
In an embodiment of the present invention, this method further includes being constructed respectively using the output and residual error time series of observer
Hankel matrixes, the rectangular projection using deterministic system and singular value decomposition method, effective Identification of Power System reduced-order model,
The frequency, damping ratio and modal parameters information of accurate extraction low-frequency oscillation dominant mode, are implemented as follows：
Step S21, according to observer/kalman filter models, the Hankel matrix equations of following recursive form are constructed：
Γ=[C CA CA2 … CAi-1]T
Wherein,And EhThe Hankel matrixes that respectively observer output and residual sequence are constituted, HtTo be filtered comprising Kalman
The Toeplitz lower triangular matrixs of wave device Markov parameters, Γ are extension Observable matrix,Estimate for the state of Kalman filtering
Meter；
Step S22, by matrixProject to EhOrthocomplement, orthogonal complementOn, i.e.,：
Wherein,Representing matrix row space projection is to matrix EhRow orthogonal space is mendedOn projection operator；In formulaMultiply behind both endsDue toThen above formula can be rewritten as：
Step S23, to formulaLeft end carries out SVD operations：
In formula, U1It isOne group of orthogonal basis on column space；
Step S24, according to known to subspace projection theory：Column vector U1For the considerable matrix Γ estimators of broad sense, it is
System matrix A can be found out by following formula：
And U1Representing matrix U respectively1Remove the matrix after last column and the first row；
Step S25, signal sampling time interval is set as Δ t, in the eigenvalue λ for seeking matrix AiAfter (i=1,2 ..., n),
Each modal parameter frequency f of the system of can geti, attenuation factoriAnd dampingratioζiInformation：
Step S26, Mode ShapeBy the right feature vector φ of sytem matrix AiIt obtains：
Compared to the prior art, the invention has the advantages that：The method of the present invention is in electric system stochastic model
Embedded observer, is effectively estimated observer Markov parameters and residual sequence, and electric system stochastic system identification problem is converted
For the identification problem of deterministic system, and introduced observer is equivalent to Kalman filter；Feature based on sciagraphy
Realize the dominant mode parameter information of extraction low-frequency oscillation of electric power system；The method of the present invention has identification precision height, strong robustness
The characteristics of, will be a kind of practicable method in wide area power system stability analysis research.
Description of the drawings
Fig. 1 is the work flow diagram of the embodiment of the present invention.
Fig. 2 is the design sketch that the method for the present invention recognizes Oscillatory mode shape.
Specific implementation mode
Below in conjunction with the accompanying drawings, technical scheme of the present invention is specifically described.
One kind of the present invention being based on O3The low-frequency oscillation of electric power system discrimination method of KID algorithms, in the random mould of electric system
Embedded observer, utilizes O in type3The Markov parameters and residual error of KID algorithms fundamental equation and Least Square Method observer,
The identification of electric system stochastic system is converted to the identification problem of deterministic system, introduced observer is equivalent to Kalman's filter
Wave device.
Carry out preferred observation signal.In addition to leading Oscillatory mode shape, while there is also other a variety of oscillation modes for power grid.Cause
This, needs the measuring signal for selecting leading Oscillatory mode shape ornamental good to carry out model analysis, and it is accurate to improve leading Oscillatory mode shape identification
True property.Sample frequency 20Hz, simulation time 30s are set, 15db white Gaussian noises will be added in selected preferred signals, set mould
Type order n=20, parameter p=30, proceed as follows：
Utilize the Markov parameters and residual error of O3KID algorithms fundamental equation and Least Square Method observer：
Step 1：Build the output observer model of following form：
Wherein,WithThe respectively state vector and output vector of observer, Μ are observer gain matrix.
Step 2：Define output estimation error vectorObserver model described in above formula can be rewritten as：
In formula
Step 3：By above formula, recursion p-1 is walked forward, can be obtained
Wherein：
O3KID algorithms use eigenvalue assignment method, by adjusting gain matrix K, by observer sytem matrixPole
Point is configured to z-plane origin, constitutes the progressive stable state observer of least beat.From Hamilton-Cayley theorems：Meeting p
Under the conditions of ＞ ＞ n, haveFormulaIt can be reduced to：
Step 4：Above formula is substituted into formulaIn can obtain：
Y (k)=Φ v (k)+ε (k)
Φ is that observer Markov joins sequence in formula, i.e. discrete unit impulse response samples.Formula y (k)=Φ v (k)+ε (k)
Characterize linear system can measure output between autoregression relationship, for k=p, p+1 ..., l-1
Y=Φ V+E
In formula：
Y=[y (p) y (p+1) ... y (l-1)]
V=[v (p) v (p+1) ... v (l-1)]
E=[ε (p) ε (p+1) ... ε (l-1)]
Formula Y=Φ V+E are the fundamental equations of O3KID algorithms, and wherein Y and V are made of scalable system output, and E is
Output error matrix.
Step 5：The least squares estimator of observer Markov parametersIt is represented by：
Wherein, symbolThe generalized inverse of representing matrix, the error matrix estimator of outputIt can be written as：
Hankel matrixes are constructed respectively using the output and residual error time series of observer, using the orthogonal of deterministic system
Projection and singular value decomposition method, effective Identification of Power System reduced-order model, the accurate frequency for extracting low-frequency oscillation dominant mode,
Damping ratio and modal parameters information：
Step 1：According to observer/kalman filter models, the Hankel matrix equations of following recursive form are constructed：
Γ=[C CA CA2 … CAi-1]T
Wherein,And EhThe Hankel matrixes that respectively observer output and residual sequence are constituted, HtTo be filtered comprising Kalman
The Toeplitz lower triangular matrixs of wave device Markov parameters, Γ are extension Observable matrix,Estimate for the state of Kalman filtering
Meter.
Step 2：By matrixProject to EhOrthocomplement, orthogonal complementOn, i.e.,：
Wherein,Representing matrix row space projection is to matrix EhRow orthogonal space is mendedOn projection operator.In formulaMultiply behind both endsDue toThen above formula can be rewritten as：
Step 3：To formulaLeft end carries out SVD operations：
In formula, U1It isOne group of orthogonal basis on column space.
Step 4：According to known to subspace projection theory：Column vector U1For the considerable matrix Γ estimators of broad sense, system
Matrix A can be found out by following formula：
Here,WithU 1Representing matrix U respectively1Remove the matrix after last column and the first row.
Step 5：If signal sampling time interval is Δ t, in the eigenvalue λ for seeking matrix AiIt, can after (i=1,2 ..., n)
Each modal parameter frequency f of acquisition systemi, attenuation factoriAnd dampingratioζiInformation：
Step 6：Mode ShapeBy the right feature vector φ of sytem matrix AiIt obtains：
Mode 1 and mode 2 indicate that dominant mode has original signal to the regression criterion of signal close to 0 as can be seen from Figure 2
Good fitting effect, Modal Parameter Identification result are accurate.Using the dominant mode of signal fitting accuracy computation to signal fitting
Degree is 11.5803dB.
The above are preferred embodiments of the present invention, all any changes made according to the technical solution of the present invention, and generated function is made
When with range without departing from technical solution of the present invention, all belong to the scope of protection of the present invention.
Claims (2)
1. one kind being based on O3The low-frequency oscillation of electric power system discrimination method of KID algorithms, which is characterized in that in the random mould of electric system
Embedded observer, utilizes O in type3The Markov parameters and residual error of KID algorithms fundamental equation and Least Square Method observer,
The identification of electric system stochastic system is converted to the identification problem of deterministic system, introduced observer is equivalent to Kalman's filter
Wave device；It is described to utilize O3The Markov parameters and residual error of KID algorithms fundamental equation and Least Square Method observer it is specific
Realization process is as follows：
Step S1, the output observer model of following form is built：
Wherein,WithThe respectively state vector and output vector of observer, Μ are observer gain matrix；
Step S2, output estimation error vector is definedThe observer model of formula (1) can be rewritten as：
In formula
Step S3, by formula (2), recursion p-1 is walked forward, can be obtained：
Wherein：
O3KID algorithms use eigenvalue assignment method, by adjusting gain matrix K, by observer sytem matrixPOLE PLACEMENT USING
To z-plane origin, the progressive stable state observer of least beat is constituted；From Hamilton-Cayley theorems：Meeting p ＞ ＞ n items
Under part, haveTherefore formula (3) can be reduced to：
Step S4, substituting into formula (4) in formula (3) can obtain：
Y (k)=Φ v (k)+ε (k) (5)
Φ is that observer Markov joins sequence in formula, i.e. discrete unit impulse response samples；Formula (5) characterizes linear system and can measure
The autoregression relationship between output is surveyed, for k=p, p+1 ..., l-1
Y=Φ V+E
In formula：
Y=[y (p) y (p+1) ... y (l-1)]
V=[v (p) v (p+1) ... v (l-1)]
E=[ε (p) ε (p+1) ... ε (l-1)]
Formula Y=Φ V+E are the fundamental equations of O3KID algorithms, and wherein Y and V are made of scalable system output, and E is output
Error matrix；
Step S5, the least squares estimator of observer Markov parametersIt is represented by：
Wherein, symbolThe generalized inverse of representing matrix, the error matrix estimator of outputIt can be written as：
Observer Markov parametersIt is uniquely determined by scalable system output time series, output errorAnd it can estimate
, thus convert the identification of electric system stochastic system to deterministic system identification problem.
2. according to claim 1 a kind of based on O3The low-frequency oscillation of electric power system discrimination method of KID algorithms, feature exist
In this method further includes constructing Hankel matrixes respectively using the output and residual error time series of observer, using certainty system
The rectangular projection of system and singular value decomposition method, effective Identification of Power System reduced-order model are accurate to extract the leading mould of low-frequency oscillation
The frequency, damping ratio and modal parameters information of state, are implemented as follows：
Step S21, according to observer/kalman filter models, the Hankel matrix equations of following recursive form are constructed：
Γ=[C CA CA2 … CAi-1]T
Wherein,And EhThe Hankel matrixes that respectively observer output and residual sequence are constituted, HtTo include Kalman filter
The Toeplitz lower triangular matrixs of Markov parameters, Γ are extension Observable matrix,For the state estimation of Kalman filtering；
Step S22, by matrixProject to EhOrthocomplement, orthogonal complementOn, i.e.,：
Wherein,Representing matrix row space projection is to matrix EhRow orthogonal space is mendedOn projection operator；In formulaMultiply behind both endsDue toThen above formula can be rewritten as：
Step S23, to formulaLeft end carries out SVD operations：
In formula, U1It isOne group of orthogonal basis on column space；
Step S24, according to known to subspace projection theory：Column vector U1For the considerable matrix Γ estimators of broad sense, system square
Battle array A can be found out by following formula：
WithU 1Representing matrix U respectively1Remove the matrix after last column and the first row；
Step S25, signal sampling time interval is set as Δ t, in the eigenvalue λ for seeking matrix AiAfter (i=1,2 ..., n), it can obtain
Obtain each modal parameter frequency f of systemi, attenuation factoriAnd dampingratioζiInformation：
Step S26, Mode ShapeBy the right feature vector φ of sytem matrix AiIt obtains：
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| CN109753689A (en) * | 2018-12-10 | 2019-05-14 | 东北电力大学 | A kind of online identifying approach of electric system electromechanical oscillations modal characteristics parameter |
| CN110083060A (en) * | 2019-04-09 | 2019-08-02 | 河南工业和信息化职业学院 | A kind of optimal output controller control method of discrete linear systems information fusion |
| CN110413943A (en) * | 2019-08-06 | 2019-11-05 | 海洋石油工程股份有限公司 | The recognition methods of offshore platform structure modal parameter |
| CN111384717A (en) * | 2020-01-15 | 2020-07-07 | 华中科技大学 | Adaptive damping control method and system for resisting false data injection attack |
| CN111797500A (en) * | 2020-06-02 | 2020-10-20 | 上海卫星工程研究所 | Solar cell array modal identification method based on standard variable analysis and improved SSI |
| CN113010844A (en) * | 2021-03-09 | 2021-06-22 | 东北电力大学 | Participation factor calculation method based on subspace dynamic mode decomposition |
| CN116632864A (en) * | 2023-05-31 | 2023-08-22 | 东北电力大学 | Ultra-low frequency oscillation control method based on parameter switching of speed regulator under environmental excitation |
| CN116973770A (en) * | 2023-09-25 | 2023-10-31 | 东方电子股份有限公司 | Battery SOC estimation method and system based on steady-state Kalman filter |
| CN117706933A (en) * | 2023-12-18 | 2024-03-15 | 兰州理工大学 | Multi-target complementary robust control method of piezoelectric positioning system |
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| CN109753689A (en) * | 2018-12-10 | 2019-05-14 | 东北电力大学 | A kind of online identifying approach of electric system electromechanical oscillations modal characteristics parameter |
| CN110083060B (en) * | 2019-04-09 | 2022-03-01 | 河南工业和信息化职业学院 | Discrete linear system information fusion optimal output regulator control method |
| CN110083060A (en) * | 2019-04-09 | 2019-08-02 | 河南工业和信息化职业学院 | A kind of optimal output controller control method of discrete linear systems information fusion |
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| CN111384717A (en) * | 2020-01-15 | 2020-07-07 | 华中科技大学 | Adaptive damping control method and system for resisting false data injection attack |
| CN111797500A (en) * | 2020-06-02 | 2020-10-20 | 上海卫星工程研究所 | Solar cell array modal identification method based on standard variable analysis and improved SSI |
| CN111797500B (en) * | 2020-06-02 | 2023-07-14 | 上海卫星工程研究所 | Solar cell array modal identification method based on canonical variable analysis and improved SSI |
| CN113010844A (en) * | 2021-03-09 | 2021-06-22 | 东北电力大学 | Participation factor calculation method based on subspace dynamic mode decomposition |
| CN113010844B (en) * | 2021-03-09 | 2022-11-11 | 东北电力大学 | Participation factor calculation method based on subspace dynamic mode decomposition |
| CN116632864A (en) * | 2023-05-31 | 2023-08-22 | 东北电力大学 | Ultra-low frequency oscillation control method based on parameter switching of speed regulator under environmental excitation |
| CN116632864B (en) * | 2023-05-31 | 2024-04-19 | 东北电力大学 | Ultra-low frequency oscillation control method based on parameter switching of speed regulator under environmental excitation |
| CN116973770A (en) * | 2023-09-25 | 2023-10-31 | 东方电子股份有限公司 | Battery SOC estimation method and system based on steady-state Kalman filter |
| CN116973770B (en) * | 2023-09-25 | 2023-12-08 | 东方电子股份有限公司 | Battery SOC estimation method and system based on steady-state Kalman filter |
| CN117706933A (en) * | 2023-12-18 | 2024-03-15 | 兰州理工大学 | Multi-target complementary robust control method of piezoelectric positioning system |
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